Sheared turbulent flows and wake dynamics of an idled floating tidal turbine

Ocean energy extraction is on the rise. While tides are the most predictable amongst marine renewable resources, turbulent and complex flows still challenge reliable tidal stream energy extraction and there is also uncertainty in how devices change the natural environment. To ensure the long-term integrity of emergent floating tidal turbine technologies, advances in field measurements are required to capture multiscale, real-world flow interactions. Here we use aerial drones and acoustic profiling transects to quantify the site- and scale-dependent complexities of actual turbulent flows around an idled, utility-scale floating tidal turbine (20 m rotor diameter, D). The combined spatial resolution of our baseline measurements is sufficiently high to quantify sheared, turbulent inflow conditions (reversed shear profiles, turbulence intensity >20%, and turbulence length scales > 0.4D). We also detect downstream velocity deficits (approaching 20% at 4D) and trace the far-wake propagation using acoustic backscattering techniques in excess of 30D. Addressing the energy-environment nexus, our oceanographic lens on flow characterisation will help to validate multiscale flow physics around offshore energy platforms that have thus far only been simulated.

) and horizontal velocity magnitude data rotated to the local coordinate system and gridded at 5D where streamlines (red) show the behaviour of the flow cross-and downstream of the O2 (upper right).Vertical distributions of horizontal velocity magnitude (lower left) and ADCP-derived backscatter (lower right).For all plots, the mean location of the O2 tidal turbine is marked with a circle (magenta).Note, the O2 was not generating with the rotors left idle.Boundary shape files: Boundary-Line™ shape files downloaded from EDINA Digimap Ordnance Survey Service.Bathymetry:©Crown Copyright/ SeaZone Solutions Limited (2022).All Rights Reserved.Not to be used for navigation.Note, figures only provide an overview and the underlying ADCP-derived current flow data is available at DOI: https://doi.org/10.24382/244fae5d-2d16-4219-98f6-7aa96757ae49 Table 1: Summary environmental information for each sampling transect for the fine-scale (red) and broad-scale (yellow) surveys.Mean velocity is the depth-mean velocity extracted from the Orbital ADCPs, averaged over the transect period, with associated standard deviation (SD).Acc denotes the acceleration in depth mean velocity from the Orbital ADCPs calculated using a linear regression over the transect period.Mean velocity and acceleration determine the Tidal State with Peak indicating strongest flows.Wind speed and direction, Wave height and Mean heading of the O2, and displacement were all measured by sensors on the platform.Wave heights less than 0.5 m should be treated with caution.Drone in-flight mean wind speed was extracted from the Airdata UAV log management system.) downstream of the O2 platform.The cross-stream extent of the bubbles associated with passing the O2 wake (time between 13:47 and 13:48 GMT) is approximately 110 m.The impacts of excess attenuation and multiple scattering are visible at the O2 wake below the bubble plume which appears to have a ''tail'' of echoes extending below the actual area of the wake, thus distorting the apparent shape and intensity of the wake.Multiple scattering can occur when the density of scatterers is high, and signals scattered from one particle are re-scattered from neighbouring particles (bouncing of echoes).In this case, the apparent wake seems to occupy the full water column, however de-noising and thresholding of the data to intensities consistent with adjacent portions of the wake was sufficient to isolate and trace the wake as per Supplementary Figure 5 and Figure 6 & 7 of the main manuscript.Small, unlabelled, and relatively intense backscatter signatures are most likely attributable to small fish or suspended biological material.Region 7 and 8 are dominated by backscatter from bubbles while region 6 and 9 correspond to scattering from suspended sediment.

Supplementary Methods 1: Large-scale Particle Image Velocimetry (LSPIV)
Lab-based particle image velocimetry (PIV) relies on seeding particles for flow visualization and velocity measurements in controlled settings.In contrast, 'Large-scale particle image velocimetry (LSPIV)' is commonly referred to when applied in natural environments such as rivers, estuaries, or oceans.LSPIV utilizes natural features or tracers for image-based or remote sensing-based velocity measurements, making it well-suited for studying largescale flows (on the order of meters) in natural water bodies.Typically Supp1-5 , LSPIV doesn't require seeding the flow with particles, instead relying on natural features or tracers present in the fluid, such as surface waves, boils, debris, foam lines Supp6 , or other high-contrast features.Unlike controlled environments such as laboratories or flumes where flows are seeded with particles, LSPIV operates in unconstrained natural settings.
Although there have been attempts to seed more constrained natural river flows with particles Supp7 , practical considerations, such as the quantity of seeds needed and the non-constrained channel flow of tidal stream sites, alongside ecological concerns, generally make this approach unfeasible.Given the ecological sensitivity of sites like tidal streams, with diverse marine fauna populations, the potential biological and ecological effects of particle releases remain unknown and are thus deemed impractical for such natural environments.Other examples of using naturally occurring tracers for PIV analysis include using natural suspended particles (sediment, plankton) and submersible PIV Supp8 to quantify turbulence in the coastal environment, and using PIV on snowflakes to study the wake of wind turbines Supp9 .
LSPIV has proven to be a valid and cost-effective image-based tool for measuring surface velocity using natural tracers in various fluvial systems, particularly in field applications.The PIV methodology relies on the crosscorrelation between small regions (or "windows") of successive images.Sufficient natural tracer features within each window are necessary to obtain good quality data, determined by the correlation threshold.Smooth water yields very low correlation values, whereas textured water yields higher correlation values.Spurious artefacts, such as sun glint, would also introduce errors that a correlation threshold alone will not remove.
We have developed and applied our own custom LSPIV analysis code to extract water surface velocity fields (speed and direction of the flow) every 0.266 s (8 frames) from each drone video sequence.We use the following simple steps to ensure robustness and reliability of the resulting velocity vector fields, without using the more advanced methods that are commonly used in laboratory-based PIV where particle seeding density and lighting are controlled to give optimal conditions.At each 0.266 s interval, four consecutive video frames (recorded at 30 fps, representing 0.1 s total duration) were used.The green colour channel (selected as most representative of the water colour) of each frame were extracted and then corrected for camera lens distortion by applying a transformation matrix prepared using the MATLAB camera calibration toolbox and a standard chequer-board technique.A simple crosscorrelation algorithm Supp10 between consecutive frames was then applied using 65 × 65 pixel windows with 50% overlap and 128-pixel clear border.This includes sub-pixel localization of the maximum correlation peak using a twodimensional quadratic function fitted through the 3x3 pixel neighbourhood.This results in fields of 20 × 39 velocity vectors extracted per frame-pair with a correlation coefficient reported for each vector indicating its quality.A minimum correlation threshold of 0.6 is applied, however for all data series reported here the minimum correlation value obtained was about 0.8.Randomly selected examples of the cross-correlation distribution in the vicinity of individual vector locations are shown in Fig. S12.Predominantly the distributions are unimodal, making a simple correlation threshold quality metric more suitable than metrics derived from multi-modal distributions (e.g.signalto-noise ratio).To reduce spurious effects from sun glint, a 3 × 3 × 3 median filter (filtering in both spatial dimensions and time) was applied across the three vector fields extracted from the four consecutive video frames providing one clean velocity field every 0.25 s through the video sequence that were then scaled according to the drone's altitude.Each 2-min hover results in about 500 clean velocity fields.As shown by the continuous distributions of pixel displacements in Fig. S13, the combination of selected window size, pixel resolution and relative scale of natural features delivers data unaffected by "pixel locking" artifacts (strong bias to integer pixel displacements) that can impact PIV measurements using poorly resolved seeded tracer particles.

Supplementary Methods 2: Turbulence length scales
We have explored two possible methods to estimate the turbulence length scale (Lu) from the PIV data.Firstly, following Supp11 , we apply Taylor's frozen field to individual vector locations, calculating the autocorrelation function (Ru,x(t)) and then applying alongstream spatial averaging prior to integration up to the 1/ crossing (Figure S14 (left) and equation 8 in [Supp11]): Secondly, we use the spatial nature of the PIV data to estimate Lu by calculating the mean correlation as a function of streamwise separation (Ru,x(X)) prior to integration up to the separation needed for the correlation curve to decrease to 1/ (Figure S14 (right)).The 1/ threshold has been previously used Supp11 in cases where the correlation function does not cross the horizontal axis due to random velocity fluctuations.Under some circumstances, the correlation still does not drop below this threshold, in which case it is not possible to return a value for Lu.
As seen in Figure S15, the two different methods for estimating Lu provide some differences in results.During the ebb flow at the inflow location (Fig. S15 left) the two estimates are generally in good agreement in the cross-stream extent, with elevated values closer to the Eday shear line (positive Y) directly corresponding to later crossing of the 1/ threshold for the shear-line curves in Figure S14.However, within the wake (Fig. S15 right, Y = -25 to 25 m) there are large differences, with elevated Lu values using the spatial method and maybe even a decrease in turbulence length scale when calculated using Taylor's frozen field.This indicates that at a single cross-stream location within the wake, the nature of the turbulence leads to rapid temporal decorrelation but has higher alongstream spatial correlation.

Supplementary Methods 3: Assessment of Drone Stability and impact on turbulence parameters
In order to assess the stability of the drone during each sampling hover used for LSPIV analysis, we have followed the procedure of [Supp12].Briefly, the drone utilised during the surveys was re-flown over a static, textured scene (cobble beach).The in-flight wind conditions, extracted from the Airdata UAV log management system that applies a drone-model specific aerodynamic model to the flight metrics, during this test flight are compared to those encountered during the surveys in Table S2.Importantly, we report both the mean and standard deviation of the wind speed derived from the UAV logs at 5 s intervals throughout the hovers.It can be seen that the test flight conditions were more extreme (in both mean speed and variation, or gusts) than encountered during the surveys.The horizontal and vertical stability of the drone is indicated by the standard deviation of the position and altitude as well as their maximum horizontal and vertical displacements during the hover (see Table S2).The yaw stability of the drone is indicated by the standard deviation in heading.Throughout the surveys when the gusts were weak (Std of wind<0.4m/s), the variations in drone position, altitude and yaw are much smaller than under the strong gusts (Std of wind>2.5 m/s) of the subsequent test flight, highlighting the importance of including gusts in these drone stability assessments.
The recorded video of the static scene was analysed using our LSPIV method detailed above to provide a direct measure of the velocity contamination from drone movement under these extreme test conditions.The resulting root mean square (RMS) velocity fluctuation within the central section of the field of view is 0.149 ms -1 .This increases to 0.195 ms -1 at the peripheries of the sample area where the combined effects of vertical and rotational movements are most pronounced.Therefore, a reasonable and conservative sensitivity threshold can be determined, for example for Turbulence Intensity, by comparing the RMS velocity fluctuation value obtained under these extreme test conditions to the typical mean flow speeds encountered during the surveys (of order 2ms -1 ), resulting in a TI sensitivity threshold of 0.149 ms -1 / 2 ms -1 = 0.075.

Fig. 2 :Fig. 3 :
Fig. 2: Overview of additional ADCP inflow transect lines.Transects showing absolute streamwise horizontal velocity (|U| ms -1 ) upstream (100 m or 5D) of the O2.For reference, the downstream location of the O2 is superimposed (hull structure, rotor arms and rotor-swept area).Note, figures only provide an overview and the underlying ADCP-derived current flow data (including the entire transect rather than just the inflow line) is available at DOI: https://doi.org/10.24382/244fae5d-2d16-4219-98f6-7aa96757ae49

Fig. 4 :
Fig. 4: PIV-derived surface current magnitude and turbulence experienced by the O2 during flood flow.A Oblique aerial drone image approaching the O2 platform during flood flow (17/04/2022, flood velocity = 3.2 ms -1 ).B Aerial image of drone hover field of view (T1, hover 2, altitude=65 m) over the O2.C Mean flow field coloured by horizontal velocity magnitude with velocity vectors overlaid and (D), turbulence intensity (TI), as calculated from the 2-min hover.Note, the O2 has been masked.E Spatial and temporal mean horizontal velocity magnitude and (F), turbulence intensity both calculated across the region bounded by dashed, white lines in C and D, highlighting the difference in horizontal velocity magnitude and TI on either side of the platform.The dashed lines in F are the turbulence length scales Lu(X) normalised by the rotor diameter D. Regions of (G) vorticity (positive = anti-clockwise) and (H), divergence (positive = upwelling) and convergence (negative = downwelling) on either side of the O2.The local coordinate system is centred around the mean O2 location.

Fig. 5 : 1 )
Fig. 5: Wake isolation and tracing using EK80 backscatter (Sv) from fine-scale transects.A Echogram of 200 kHz pre-processed data during ebb tide (17/04/2022, T5, mean ebb velocity= 2.8 ms -1 ) showing mean volume backscattering strength (Sv; dB re 1m - 1 ) as a function of depth (y axis) and time (x axis), with bad pings and seabed removed.The transect started downstream of the turbine (D5-D1) and ended with an upstream line (U), with the O2 being passed at about 13:05 (GMT).The colour bar represents the range of Sv values displayed in all echograms.B Denoising algorithm-processed echogram showing integrated mean volume backscatter strength data (gridded at a resolution of 5 pings along the track by 0.5 m depth bins).C Image-processed Sv data isolating and visualising surface-connected bubble entrainment by macro-turbulence using a -50 dB threshold.Highlighted in white are the cross-stream sections (Y=±100 m) of the transect in-line with the O2 platform.D Mean Sv within surface-connected bubble plume isolated in C. E Area (/1000; in m 2 ; left y-axis) and maximum backscattering strength (Sv; right y-axis) of bubble plume within each highlighted section.F Mean cross-stream (Y) location of the surface-connected bubble plume within each section, the O2 is located at Y=0.

Fig. 6 :Fig. 7 :
Fig. 6: Fine-scale transect extending 1600 m downstream of the O2 during ebb tidal flows.A Depth-averaged horizontal velocity with vectors coloured by magnitude (14/04/2022, T4, mean ebb velocity = 2.55 ms -1 ).B Vertical distributions of ADCPderived backscatter, a proxy for surface-connected bubble entrainment by macro-turbulence C, D Corresponding horizontal velocity magnitude and ADCP backscatter data rotated to the local coordinate system and gridded at 1D. Streamlines (red) show the behaviour of the flow cross-and downstream of the O2.For all plots, the mean location of the O2 tidal turbine is marked with a circle (magenta).Note, the strong scattering visible in the backscatter data in D (X=-1400-1600) is associated with the OpenHydro turbine installed in 2006 (marked with a black circle in A & B), consisting of two steel monopoles drilled into the seabed.The OpenHydro platform generated its own wake penetrating approximately 15 m deep over 30 m overall water depth.This is best visualised in D at x=-1300 to x= -1600 m.Boundary shape files: Boundary-Line™ shape files downloaded from EDINA Digimap Ordnance Survey Service.Bathymetry:©Crown Copyright/SeaZone Solutions Limited (2022).All Rights Reserved.Not to be used for navigation.Note, figures only provide an overview and the underlying ADCP-derived current flow data is available at DOI: https://doi.org/10.24382/244fae5d-2d16-4219-98f6-7aa96757ae49

Fig. 8 :
Fig. 8: PIV-derived surface current magnitude and turbulence across the O2 wake during flood flow.A Oblique aerial drone image approaching the O2 platform during flood flow (17/04/2022, mean flood velocity = 3.2 ms -1 ).B Aerial image of drone hover field of view (T1, hover 4, altitude=65 m) over the O2 wake (5.5D downstream) C Mean flow field coloured by horizontal velocity magnitude with velocity vectors overlaid and (D), turbulence intensity (TI), as calculated from the 2-min hover.E Spatial and temporal mean horizontal velocity magnitude and (F), turbulence intensity both calculated across the region bounded by dashed, white lines in C and D, highlighting the difference in horizontal velocity magnitude and TI across the wake area and adjacent to either side of the wake.The dashed lines in F are the turbulence length scales Lu(X) normalised by the rotor diameter D. Regions of (G) vorticity (positive = anti-clockwise) and (H), divergence (positive = upwelling) and convergence (negative = downwelling) on either side of the O2 (frame=237, same as in B).The local coordinate system is centred around the mean O2 location.

Fig. 9 :Fig. 10 :
Fig. 9: Survey vessel transect lines during fine-scale surveys.Positions for all transect lines extracted from the ADCP data files (recorded at 4.22s intervals) showing the streamwise and cross-stream variations in surveys.Largest variation in transect line locations and orientation were during initial scoping transects on the 13 th (dark blue points).Transect lines on the 14 th and 17 th that followed pre-defined waypoints are more tightly clustered at 100 m intervals upstream and downstream of the O2 location (magenta).The inset plot shows the overall excursion of the O2 platform during the entire sampling period.Note, the underlying data is available at DOI: https://doi.org/10.24382/244fae5d-2d16-4219-98f6-7aa96757ae49

Fig. 11 :
Fig. 11: Convergence of flow parameters derived from PIV data.Cumulative mean over time of the velocity magnitude (left) and cumulative turbulence intensity (right), both spatially-averaged in the alongstream-direction (thick lines) between the white dashed lines on Figure S3C, from two different individual Y locations showing good convergence of the values in the freestream (FS, Y= -38 m), and less good convergence in the shear line (S, Y= 38 m), by which time the total number of samples incorporated is 2,868.The individual data series that comprise the spatial average are shown by the associated thin lines, comprising a maximum of 478 samples each.

Fig. 12 :
Fig. 12: Spatial (pixel space) distributions of cross-correlation at 25 randomly selected instantaneous vector locations upstream of the O2.The determination of the cross-correlation peak location provides the inter-frame displacement and hence velocity.Filled contours are at correlation intervals of 0.1 with values given by the colour bar.Ebb flow transects on 17/04/2022 (T6, hover 1, altitude=65 m).

Fig. 13 :
Fig.13: Histograms of measured cross-correlation peak displacement to assess peak-locking.Histograms of LSPIV-derived displacement data (pixels) from which velocity vectors are determined upstream of the O2 (17/04/2022, T6, hover 1).The upper panels show all vector locations and time intervals for an entire 2-min hover, while the lower panels show all vector locations at 10 random time instants within the same hover.